Focus: Magnet Theory Meets Earthquakes

Mathematical tools from the theory of magnets applied to seismic data reveal that the stronger an earthquake, the sooner the next one will occur, and it could be hundreds of miles away.

The time you’ll most likely see an earthquake is soon after another earthquake, even if it occurred hundreds of miles away, according to several studies. Now a paper in the 8 July PRL quantifies this idea by showing that the stronger an earthquake, the sooner there will be another one. A Spanish researcher uncovered this relationship by studying seismic data using mathematical tools from the physics of solids that were inspired by quantum theory. The paper concerns the statistical properties of earthquakes, so it does not provide a magic formula to predict where and when a quake will occur.

Combing through global seismic data, theorists have discovered in recent years that earthquakes tend to come in clusters–large numbers of events close in time–and that they follow a “self-similarity,” or “fractal,” principle: A cluster is most likely to occur soon after another cluster; a cluster of clusters after another cluster of clusters, and so on. If you plot thousands of events worldwide as dots on a timeline, the clustering that shows up on a year’s worth of data looks very similar to a decade’s worth of data where the dots represent clusters. The similarity extends to the century scale, if you again replace clusters with single dots. This is a bit like comparing the coastline of Africa with that of a tiny island–often the “roughness” of the coastline is similar, regardless of the scale of the map.

Álvaro Corral of the Autonomous University of Barcelona looked at seismic data in analogy with another case of self-similarity in nature, the critical magnetization of a metal. A metal becomes magnetic when clusters of atoms feel one another’s magnetic forces and align their magnetic moments in the same direction, like a collection of tiny arrows all adding up to one big arrow. If you heat them up, the arrows jiggle more and more, and at very high temperatures, they all point in random directions.

But at an intermediate, “Curie” temperature, they can still feel one another’s magnetism and form aligned clusters, although each cluster points in a random direction. At this special temperature, there are clusters and “superclusters” of all sizes. The configuration looks the same if you “zoom in” to the atomic scale or “zoom out” to the macroscopic scale. This self-similarity allows researchers to use a mathematical tool orignally from quantum theory called the renormalization group, the mathematical representation of the “zoom” operations.

Corral realized that the same tool could be applied to seismic data. Researchers knew that after a major quake, earthquakes are more likely in a wider region than that affected by aftershocks, but no one had quantified the relationship. Corral used renormalization to look at data from many time scales all at once. His model predicts that the stronger an earthquake, the sooner the next one will occur. He believes that a future, more complex model could show that the whole recent history matters, not just the last event.

However, he says, his model suggests no correlation with the likely magnitude of the next earthquake. “Earthquakes know when they will happen, but they don’t know what magnitude they are going to be,” he says. This notion contradicts the commonly held belief that a large earthquake today means a long wait before the next large earthquake.

Norman Sleep of Stanford University in California says the paper is a useful step in understanding earthquakes. The fact that earthquakes come in clusters has a physical explanation, he says: “A large earthquake can trigger another large earthquake on a nearby fault where the static stress increased.”

–Davide Castelvecchi

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Expect more. After the magnitude 6.7 Northridge earthquake in 1994, further quakes were likely to follow quickly, even beyond the local area of aftershocks, according to research that borrows mathematical tools from the study of magnetism.